A Bayesian Approach for Joint Modeling of Skew-Normal Longitudinal Measurements and Time to Event Data

Abstract

Joint modeling of longitudinal measurements and survival time has an important role in analyzing medical data sets. For example, in HIV data sets, a biological marker such as CD4 count measurements is considered as a predictor of survival. Usually, longitudinal responses of these studies are severely skew. An ordinary method for reducing the skewness is the use of square root or logarithm transformations of responses. In most of the HIV data sets, because of high rate of missingness, skewness is remained even after using the transformations. Therefore, a general form of distributions for considering skewness in the model should be used. In this paper, we have used multivariate skew-normal distribution to allow a flexible model for considering non-symmetrically of the responses. We have used a skew-normal mixed effect model for longitudinal measurements and a Cox proportional hazard model for time to event variable. These two models share some random effects. A Bayesian approach using Markov chain Monte Carlo is adopted for parameter estimation. Some simulation studies are performed to investigate the performance of the proposed method. Also, the method is illustrated using a real HIV data set. In these data, longitudinal outcomes are skew and death is considered as the event of interest. Different model structures are developed for analyzing this data set, where model selection is performed using some Bayesian criteria.